1. Field of the Invention
The invention relates to measuring parameters of interest in a downhole environment. More specifically, the invention is an apparatus and method for determining resistivities values and relative dip in an anisotropic borehole formation.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that, when properly interpreted, are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p.148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517 issued to Barber; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
U.S. Pat. No. 5,452,761 to Beard et al., the contents of which are fully incorporated herein by reference, discloses an apparatus and method for digitally processing signals received by an induction logging tool having a transmitter and a plurality of receivers. An oscillating signal is provided to the transmitter, which causes eddy currents to flow in a surrounding formation in the frequency domain, transient domain or a combination of both. The magnitudes of the eddy currents are proportional to the conductivity of the formation. The eddy currents in turn induce voltages in the receivers. The received voltages are digitized at a sampling rate well above the maximum frequency of interest. Nyquist sampling criteria specifies the sampling frequency to be at least twice the maximum frequency present in the signal being digitized in order to avoid aliasing distortion of the digitized signal. The digitizing window is synchronized to a cycle of the oscillating current signal. The oscillating current could be a combination of sinusoidal frequencies for a survey in the frequency domain or a repetitive transient current source for a survey in the transient domain. For the later the measured data would be transformed to the frequency domain for resistivity measurement data analysis, processing, inversion to define resistivity properties and structural characteristics of an earth formation resistivity model. Corresponding samples obtained in each cycle are cumulatively summed over a large number of such cycles. The summed samples form a stacked signal. Stacked signals generated for corresponding receiver coils are transmitted to a computer for spectral analysis. Transmitting to the surface the stacked signals and not all the individually sampled signals, reduces the amount of data that needs to be stored or transmitted. A Fourier analysis is performed of the stacked signals to derive the amplitudes of in-phase and quadrature components of the receiver voltages at the frequencies of interest. From the component amplitudes, the conductivity of the formation can be accurately derived.
A limitation to the electromagnetic induction resistivity well logging instruments such as that discussed in Beard et al. is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art, these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones that are typically hydrocarbon-bearing and are of the most interest to the instrument user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art.
U.S. Pat. No. 6,147,496 to Strack et al. teaches the use of an induction logging tool in which at least one transmitter and at least one receiver with orientation limited to orthogonal directions. By performing measurements with the tool with at least two different frequencies, it is possible to substantially reduce the effect of borehole and invasion and to determine the orientation of the tool to the bedding planes.
U.S. Pat. No. 5,999,883 issued to Gupta et al. (the xe2x80x9cGupta patentxe2x80x9d), the contents of which are fully incorporated here by reference, discloses a method for determining the horizontal and vertical conductivity of anisotropic earth formations. Electromagnetic induction signals induced by induction transmitters oriented along three mutually orthogonal axes are measured. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of this magnetic moment perpendicular to the orthogonal axes is calculated from the receiver signal including the signals measured perpendicular to the instrument axis. An intermediate measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation corresponding to a first coordinate transformation. A relative angle of inclination of one of the orthogonal axes which is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to a direction of the vertical conductivity. The initially rotated magnitudes are rotated through a negative of the angle of inclination corresponding to the a coordinate transformation. The resistivity anisotropy evaluation is referenced to the principal axis of transverse anisotropy (in a simpler case) and the bedding plane. A similar procedure for a more general case could address the case of biaxial anisotropy in layered media where Rhx differs from Rhy. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second step of rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second step of rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter.
U.S. patent application Ser. No. 09/676,097 by Kriegshauser et al, the contents of which are fully incorporated herein by reference, discusses the use of a multi-component induction logging tool in which five components of the magnetic field are recorded. This tool, which is marketed under the name 3DEX(trademark) by Baker Hughes Inc., measures three principal components Hxx, Hyy, Hzz and two cross-components Hxy and Hxz. The measured data from 3DEX(trademark) tool are unfocused and thus inversion is necessary in interpreting the 3DEX(trademark) data.
The 3DEX(trademark) device contains three transmitters and three receivers directed along orthogonal axes (x, y, z) with the z-component along the longitudinal axis of the drilling tool. The 3DEX(trademark) device gives knowledge of resistivities and provides a process for general inversion of data. 3DEX(trademark) is useful in determining orientation, given a sufficient selection of initial conditions. However, the 3DEX(trademark) device collects data from the non-invaded zone to put in its model. Furthermore, the 3DEX(trademark) device is sensitive to the initial conditions used in its data inversion. There is a need to provide a method of 3DEX(trademark) data inversion with improved initial conditions to improve convergence, accuracy and stability of results.
Pending U.S. patent app. Ser. No. 10/091,310 by Zhang et al uses a method for the simultaneous inversion of measurements made by a multi-component logging tool to obtain a layered resistivity model and formation inclination angle and azimuth. A model that includes horizontal and vertical resistivities is used to generate a simulated tool response. An iterative solution that gives an improved match between the model output and the field observations is obtained using a global objective function. The global objective function is defined as a sum of a data objective function (difference between the model output and the observed data) and a model objective function that stabilizes the inversion procedure by placing a penalty on large changes in the model at each iteration. The measurements may be made by an electromagnetic logging tool having an axis inclined to the normal to the bedding planes of the formation. The logging tool includes transmitters and/or receivers with coils inclined to the axis of the tool. In a preferred embodiment of the invention, the data objective function is defined in the coil coordinate system. Surveying of the borehole and orientation sensors on the tool provides the necessary information for rotating the model output to the coil coordinate system.
In a technical paper entitled xe2x80x9cA New Method to Determine Horizontal Resistivity in Anisotropic Formations Without Prior Knowledge of Relative Dip,xe2x80x9d 37th SPWLA Annual Logging Symposium, New Orleans, Jun. 16-19, 1996, Hagiwara discloses a method to determine the horizontal resistivity for deviated boreholes or dipping formations using two conventional induction-type resistivity measurements. However, Hagiwara""s method does not provide the relative dip angle. To obtain the relative dip angle, the formation anisotropy must be known. Moreover, Hagiwara shows that, for conventional induction logging tools (in which the transmitter and receiver antennas are oriented co-axially with the tool), it is impossible to obtain all three parameters (horizontal resistivity, vertical resistivity, and relative dip angle) simultaneously. The reasons such a simultaneous solution is not possible using conventional induction logging tools is that, in the response of such tools, the vertical resistivity and the relative dip angle are coupled (i.e., they are not independent).
European Patent Application No 0840142 by Wu discloses a method and apparatus for determining horizontal conductivity, vertical conductivity, and relative dip angle during a drilling operation. If the relative dip angle is unknown, Wu""s technique involves the formulation of a relationship between the dielectric constants of the formation to the anisotropic conductivities of the formation. However, in the proof by Hagiwara mentioned above, the dielectric constants are assumed quantities, and their contribution to the phase shift resistivity is minimal. Therefore, even if the dielectric constants are known, the vertical resistivity and the relative dip angle are still coupled and do not allow for a simultaneous solution.
U.S. Pat. No. 6,136,155, issued to Bittar, discloses an apparatus and method for determining resistivities in a downhole environment. The invention of Bittar ""155 is directed to an improved downhole method and apparatus for simultaneously determining the horizontal resistivity, vertical resistivity, and relative dip angle for anisotropic earth formations. The antenna configuration in which a transmitter antenna and a receiver antenna are oriented in non-parallel planes such that the vertical resistivity and the relative dip angle are decoupled. Preferably, either the transmitter or the receiver is mounted in a conventional orientation in a first plane that is normal to the tool axis, and the other antenna is mounted in a second plane that is not parallel to the first plane. Although this invention is primarily intended for MWD or LWD applications, it is also applicable to wireline and possible other applications.
The method of Bittar ""155 is designed using a two-dimensional geometry which does not include the relative azimuthal position of the measurements in the borehole needed to be considered in order to uniquely resolve the orientation of the principle axis of anisotropy and to consequently resolve Rh, Rv and the relative dip. A three-dimensional measurement system is required to properly observe and interpret the resistivity tensor and define its orientation in an anisotropic media. Bittar ""155 neglects the azimuthal position of the measurements necessary to resolve the principal axis of anisotropy even for the simple case of transverse anisotropy (TI). The outlined method for measuring horizontal magnetic dipole and vertical magnetic dipole further demonstrate the specifications to be two-dimensional and neglects the azimuthal position of the measurements necessary to resolve the principal axis of anisotropy, even for the simple case of transverse anisotropy. Computed and measured resistivities associated with the induced voltages of Bittar ""155 do not have the necessary parameterization to properly and accurately describe the measurements and their respective position with respect to the observed resistivity tensor direction. The present invention addresses the shortcomings of Bittar ""155.
There is a need for a fast and robust method for determination of a stable and unique anisotropy solution in conductive borehole environments. A three-dimensional measurement system is required to properly observe and interpret the resistivity tensor in an anisotropic media. The present invention satisfies this need.
The present invention is an apparatus and method for a determining a resistivity property of earth formation penetrated by a borehole. A plurality of multi-component resistivity sensors on a logging tool are used for obtaining measurements at a plurality of tool-face angles of said logging tool within the borehole. The measurements made by the resistivity sensors are represented by an associated function (such as a sinusoid) of the tool-face angles. The resistivity property is derived from these functions. The logging tool may be conveyed into the borehole on a wireline or a drilling tubular. The toolface angles may be obtained with an orientation sensor such as a magnetometer, accelerometer, or gyroscope.
Measurements made at a plurality of depths may be analyzed jointly. This, together with binning of the data, particularly when measurements are made while drilling, can improve the signal-to-noise ratio, thus improving the determination of resistivity.